Answers

It depends which partition we are talking about: if OS partition, yes, server will "crash". If data or log file partition, SQL Server will not crash but the DB will be in suspect state. It is a best practice to monitor the free disk space along with
some other options for databases.

If disk space may full for master or any other system databases that is basically a design failure. You never ever put system databases to the same partition where user databases are stored in production environment. Monitoring disk usage for system dbs
are also worth to do.

Janos

There are 10 type of people. Those who understand binary and those who do not.
My Blog

It depends which partition we are talking about: if OS partition, yes, server will "crash". If data or log file partition, SQL Server will not crash but the DB will be in suspect state. It is a best practice to monitor the free disk space along with
some other options for databases.

If disk space may full for master or any other system databases that is basically a design failure. You never ever put system databases to the same partition where user databases are stored in production environment. Monitoring disk usage for system dbs
are also worth to do.

Janos

There are 10 type of people. Those who understand binary and those who do not.
My Blog